Section 3: library functions
slasd5.f – Synopsis Functions/Subroutines subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK) SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA,…
slasd4.f – Synopsis Functions/Subroutines subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension(…
slasd3.f – Synopsis Functions/Subroutines subroutine slasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO) SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix…
slasd2.f – Synopsis Functions/Subroutines subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO) SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real,…
slasd1.f – Synopsis Functions/Subroutines subroutine slasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO) SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd1 (integerNL, integerNR, integerSQRE, real, dimension( * )D, realALPHA, realBETA, real, dimension( ldu, * )U,…
slasd0.f – Synopsis Functions/Subroutines subroutine slasd0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO) SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd0 (integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real,…
slascl2.f – Synopsis Functions/Subroutines subroutine slascl2 (M, N, D, X, LDX) SLASCL2 performs diagonal scaling on a vector. Function/Subroutine Documentation subroutine slascl2 (integerM, integerN, real, dimension( * )D, real, dimension( ldx, * )X, integerLDX) SLASCL2 performs diagonal scaling on a vector. Purpose: SLASCL2 performs a diagonal scaling on a vector: x <– D * x…
slascl.f – Synopsis Functions/Subroutines subroutine slascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO) SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. Function/Subroutine Documentation subroutine slascl (characterTYPE, integerKL, integerKU, realCFROM, realCTO, integerM, integerN, real, dimension( lda, * )A, integerLDA, integerINFO) SLASCL multiplies a general rectangular matrix by a…
slas2.f – Synopsis Functions/Subroutines subroutine slas2 (F, G, H, SSMIN, SSMAX) SLAS2 computes singular values of a 2-by-2 triangular matrix. Function/Subroutine Documentation subroutine slas2 (realF, realG, realH, realSSMIN, realSSMAX) SLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: SLAS2 computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H…
slarzt.f – Synopsis Functions/Subroutines subroutine slarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) SLARZT forms the triangular factor T of a block reflector H = I – vtvH. Function/Subroutine Documentation subroutine slarzt (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT) SLARZT…
slarzb.f – Synopsis Functions/Subroutines subroutine slarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARZB applies a block reflector or its transpose to a general matrix. Function/Subroutine Documentation subroutine slarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt,…
slarz.f – Synopsis Functions/Subroutines subroutine slarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentation subroutine slarz (characterSIDE, integerM, integerN, integerL, real, dimension( * )V, integerINCV, realTAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK) SLARZ applies…
slaruv.f – Synopsis Functions/Subroutines subroutine slaruv (ISEED, N, X) SLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentation subroutine slaruv (integer, dimension( 4 )ISEED, integerN, real, dimension( n )X) SLARUV returns a vector of n random real numbers from a uniform distribution. Purpose: SLARUV returns a vector of n…
slartv.f – Synopsis Functions/Subroutines subroutine slartv (N, X, INCX, Y, INCY, C, S, INCC) SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. Function/Subroutine Documentation subroutine slartv (integerN, real, dimension( * )X, integerINCX, real, dimension( * )Y, integerINCY, real, dimension( * )C, real,…
slartgs.f – Synopsis Functions/Subroutines subroutine slartgs (X, Y, SIGMA, CS, SN) SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. Function/Subroutine Documentation subroutine slartgs (realX, realY, realSIGMA, realCS, realSN) SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the…
slartgp.f – Synopsis Functions/Subroutines subroutine slartgp (F, G, CS, SN, R) SLARTGP generates a plane rotation so that the diagonal is nonnegative. Function/Subroutine Documentation subroutine slartgp (realF, realG, realCS, realSN, realR) SLARTGP generates a plane rotation so that the diagonal is nonnegative. Purpose: SLARTGP generates a plane rotation so that [ CS SN ] ….
slartg.f – Synopsis Functions/Subroutines subroutine slartg (F, G, CS, SN, R) SLARTG generates a plane rotation with real cosine and real sine. Function/Subroutine Documentation subroutine slartg (realF, realG, realCS, realSN, realR) SLARTG generates a plane rotation with real cosine and real sine. Purpose: SLARTG generate a plane rotation so that [ CS SN ] ….
slarscl2.f – Synopsis Functions/Subroutines subroutine slarscl2 (M, N, D, X, LDX) SLARSCL2 performs reciprocal diagonal scaling on a vector. Function/Subroutine Documentation subroutine slarscl2 (integerM, integerN, real, dimension( * )D, real, dimension( ldx, * )X, integerLDX) SLARSCL2 performs reciprocal diagonal scaling on a vector. Purpose: SLARSCL2 performs a reciprocal diagonal scaling on an vector: x <–…
slarrv.f – Synopsis Functions/Subroutines subroutine slarrv (N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W, WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO) SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. Function/Subroutine…
slarrr.f – Synopsis Functions/Subroutines subroutine slarrr (N, D, E, INFO) SLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues. Function/Subroutine Documentation subroutine slarrr (integerN, real, dimension( * )D, real, dimension( * )E, integerINFO) SLARRR performs tests to decide whether the symmetric tridiagonal…